The story goes on. Today, I noticed, that the percentage stayed constant at 80%, although the phone was plugged in. I took a screenshot. Then, after a while, I plugged the phone off to accept a call. After the call I plugged it in, but was puzzeled because the percentage was dropped to 72%. But the picture now shows, that the percentage lowered the whole time! (the pictures are starting at the same time!)
To make the confusion perfect: the phone is now charging (without reboot)!